PAN AFRICA CHRISTIAN UNIVERSITY
DIPLOMA IN INFORMATION AND COMMUNICATION TECHNOLOGY
END OF TERM EXAMINATION
DEPARTMENT:
COMPUTING &INFORMATION TECHNOLOGY
COURSE CODE:
DICT0124
CAMPUS:
ROYSAMBU
COURSE TITLE:
OPERATIONS RESEARCH
EXAM DATE:
TUESDAY, 4TH APRIL 2017
TIME:
09:00-17:00 HRS
INSTRUCTIONS

This exam script has TWO (2) sections.

Read all questions carefully before attempting.

Answer All questions in Section A and any other Four questions in Section B.

Write onlyyour student number on the answer booklet provided.

None programmable calculators permitted

Calculators on phones, tablets and computers are NOT permitted in Theory Papers
© Copyright 2017 All Rights Reserved PAC University
PAN AFRICA CHRISTIAN UNIVERSITY
EXAMINATIONS PAPER
SECTION A
(Answer ALL questions in this section)
Question 1:
I.
Explain the term operations research.
(2 Marks)
II.
State TWO reasons for using mathematical models in operations management.
(2 Marks)
III.
Distinguish between Deterministic and Stochastic models.
(4 Marks)
IV. Outline the 7 steps of problem solving in linear programming.
(7 Marks)
V. A painter has exactly 32 units of yellow dye and 54 units of green. He plans to
mix as many gallons as possible of color A and color B. Each gallon of color A
requires 4 units of yellow dye and 1 unit of green dye. Each gallon of color B
requires 1 unit of yellow dye and 6 units of green dye. Find the maximum
number of gallons he can mix.
(5 Marks)
SECTION B
(Answer any FOUR (4) questions in this section)
Question 2:
I.
State SIX applications of operations research.
(6 Marks)
II.
A farmer can plant up to 8 acres of land with wheat and barley. He can earn
$5,000 for every acre he plants with wheat and $3,000 for every acre he plants
with barley. His use of a necessary pesticide is limited by federal regulations to
10 gallons for his entire 8 acres. Wheat requires 2 gallons of pesticide for every
acre planted and barley requires just 1 gallon per acre.
a) Formulate the dual problem.
(6 Marks)
b) Solve the dual problem using the graphical method to determine the
maximum number of gallons he can mix.
(8 Marks)
Question 3:
I.
Explain ONE advantage of using the simplex method over the graphical method
when solving linear programming problems.
(2 Marks)
II.
Outline the procedure for forming a dual linear programming problem.
(3 Marks)
III.
Form the dual of the following linear programming problem.
(5 Marks)
Minimize C = 16 x1 + 9x2 + 21x3
Subject to:
x1 + x2 + 3x3 ≥ 12
2 of 4 | P a g e s
©PAC UNIVERSITY2017
PAN AFRICA CHRISTIAN UNIVERSITY
EXAMINATIONS PAPER
IV.
2x1 + x2 +x3 ≥ 16
x1, x2, x3 ≥ 0
Solve the dual of the linear programming problem in III above using the simplex
method.
(10 Marks)
Question 4:
I.
Outline the steps used to solve a linear programming problem using the simplex
method.
(7 Marks)
II.
Explain the term slack variable as used in linear programming.
(3 Marks)
III.
The Cannon Hill furniture Company produces tables and chairs. Each table takes
four hours of labor from the carpentry department and two hours of labor from
the finishing department. Each chair requires three hours of carpentry and one
hour of finishing. During the current week, 240 hours of carpentry time are
available and 100 hours of finishing time. Each table produced gives a profit of
$70 and each chair a profit of $50. Determine the number of chairs and tables
that should be made?
(10 Marks)
Question 5:
I.
Consider a construction company building a 250-unit apartment complex. The
project consists of hundreds of activities involving excavating, framing, wiring,
plastering, painting, landscaping, and more. Some of the activities must be done
sequentially and others can be done simultaneously. Also, some of the activities
can be completed faster than normal by purchasing additional resources such as
workers or equipment.
a) Suggest assumptions that could be made to simplify the model.
(5 Marks)
b) Explain how management science could be used to solve the above
problem.
(5 Marks)
c) Outline FOUR possible uncontrollable outputs in the scenario.
(4 Marks)
d) Identify the decision variables, objective function, and constraints for
the scenario.
(6 Marks)
3 of 4 | P a g e s
©PAC UNIVERSITY2017
PAN AFRICA CHRISTIAN UNIVERSITY
EXAMINATIONS PAPER
Question 6:
I.
The following table represents a transportation problem. Use it to answer the
questions that follow:
Destination
Origin
1
2
3
4
Supply
A
11
13
17
14
250
B
16
18
14
10
300
C
21
24
13
10
400
Demand
200 225
275 250
a) Determine if the transportation problem is balanced.
(4 Marks)
b) Find the initial basic feasible solution using Vogel’s Approximation Method.
(12 Marks)
c) Suppose that the total demand was 1000 against the total supply of 950. Explain
how you would deal with the situation.
(4 Marks)
Question 7:
I.
Explain your understanding of an assignment problem.
(2 Marks)
II.
Distinguish between basic and non-basic variables.
(4 Marks)
III.
A plant manager has four subordinates, and four tasks to be performed. The
subordinates differ in efficiency and the tasks differ in their intrinsic difficulty.
This estimate of the times each man would take to perform each task is given in
the effectiveness matrix below.
A
I
8
II III IV
26 17 11
B 13 28 4 26
C 38 19 18 15
D 19 26 24 10
How should the tasks be allocated so as to minimize the total man hours?
(14 Marks)
4 of 4 | P a g e s
©PAC UNIVERSITY2017